Equation 677 Database

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Magma c4daaeb1e4ff…

magma c4daaeb1e4ff
Size
321
Isomorphism class hash
c4daaeb1e4ffb6fc6eb1c9ad3dcad98340a036ffb2a01d4ccbb9e4951d059e7a
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 320) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 22:28:40
Display reorder
300,101,25,197,245,23,99,243,26,195,21,24,244,100,196,22,97,28,193,241,19,98,29,194,242,20,96,27,192,240,18,203,31,107,251,14,201,32,105,249,12,202,30,106,250,13,34,199,103,247,17,35,200,104,248,15,33,198,102,246,16,315,313,303,305,272,42,273,275,274,265,266,43,264,267,44,270,269,268,271,256,45,257,259,258,260,46,261,262,263,252,47,253,254,255,297,40,296,299,298,288,41,289,290,291,293,39,292,295,294,36,281,280,282,283,37,285,284,286,287,38,276,277,278,279,319,317,318,320,122,9,114,221,69,120,219,10,115,70,11,220,121,116,71,125,8,117,217,68,123,6,118,218,66,124,7,119,216,67,112,1,128,227,60,113,0,126,225,61,111,2,127,226,62,3,108,131,223,63,4,109,129,224,64,5,110,130,222,65,308,312,316,301,209,57,82,136,233,207,137,58,83,231,59,135,208,81,232,205,56,78,132,229,206,54,79,133,230,204,55,80,134,228,73,48,215,142,239,74,49,213,143,237,72,50,214,141,238,51,76,211,138,235,52,77,212,139,236,53,75,210,140,234,302,311,307,310,146,85,180,179,165,144,177,86,181,166,84,178,145,182,167,149,88,183,175,164,147,89,184,176,162,148,87,185,174,163,186,91,152,170,156,187,92,150,168,157,188,90,151,169,158,94,189,155,173,159,95,190,153,171,160,93,191,154,172,161,306,314,304,309 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 321 = 1 + 5*64, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 5, B) with E = magma#48d4131c324a99301720abcc6dab4afc68cf81d40922963883b47bf0604d0986, M = {60} in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(5, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 21.

last edited by qawbecrdtey at 2026-10-01 22:28:41 · history